On normal solvability of a Dirichlet-type problem for a third-order improperly elliptic equation

2012 ◽  
Vol 57 (5) ◽  
pp. 551-565
Author(s):  
H.M. Hayrapetyan ◽  
P.E. Meliksetyan
Keyword(s):  
Elliptic Equation ◽  
Type Problem ◽  
Third Order ◽  
Normal Solvability ◽  
Dirichlet Type ◽  
Dirichlet Type Problem ◽  
Improperly Elliptic Equation

scholarly journals ON THE DIRICHLET PROBLEM TO ELLIPTIC EQUATION, THE ORDER OF WHICH DEGENERATES AT THE AXIS OF A CYLINDER

2017 ◽  
Vol 22 (5) ◽  
pp. 717-732 ◽  
Author(s):  
Stasys Rutkauskas
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Classical Solutions ◽  
Type Problem ◽  
Smooth Functions ◽  
3 Dimensional ◽  
Dirichlet Type ◽  
Dirichlet Type Problem

In this article, an elliptic equation, which type degenerates (either weakly or strongly) at the axis of 3-dimensional cylinder, is considered. The statement of a Dirichlet type problem in the class of smooth functions is given and, subject to the type of degeneracy, the classical solutions are composed. The uniqueness of the solutions is proved and the continuity of the solutions on the line of degeneracy is discussed.

ON THE FIRST BOUNDARY VALUE PROBLEM FOR THE CLASS OF ELLIPTIC SYSTEMS DEGENERATING AT AN INNER POINT

2001 ◽  
Vol 6 (1) ◽  
pp. 147-155 ◽  
Author(s):  
S. Rutkauskas
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Elliptic Systems ◽  
Second Order ◽  
Type Problem ◽  
Dirichlet Type ◽  
Holder Class ◽  
Uniqueness Of The Solution ◽  
Dirichlet Type Problem

The Dirichlet type problem for the weakly related elliptic systems of the second order degenerating at an inner point is discussed. Existence and uniqueness of the solution in the Holder class of the vector‐functions is proved.

scholarly journals The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Marcello Lucia ◽  
Michael J. Puls
Keyword(s):  
Real Number ◽  
Measure Space ◽  
Metric Measure Space ◽  
Metric Measure Spaces ◽  
Type Problem ◽  
Locally Compact ◽  
Dirichlet Type ◽  
Algebra Of Functions ◽  
Measure Spaces ◽  
Dirichlet Type Problem

Abstract Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.

scholarly journals Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yudier Peña Pérez ◽  
Ricardo Abreu Blaya ◽  
Paul Bosch ◽  
Juan Bory Reyes
Keyword(s):  
Maxwell System ◽  
Type Problem ◽  
Type Curves ◽  
Dirichlet Type ◽  
Novel Approach ◽  
Time Harmonic ◽  
Closed Type ◽  
Intimate Relations ◽  
Fractal Domains ◽  
Dirichlet Type Problem

We investigate an electromagnetic Dirichlet type problem for the 2D quaternionic time-harmonic Maxwell system over a great generality of fractal closed type curves, which bound Jordan domains in R2. The study deals with a novel approach of h-summability condition for the curves, which would be extremely irregular and deserve to be considered fractals. Our technique of proofs is based on the intimate relations between solutions of time-harmonic Maxwell system and those of the Dirac equation through some nonlinear equations, when both cases are reformulated in quaternionic forms.

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